An actuator has a rotary drive and a threaded element for converting the rotary motion of the rotary drive into a reciprocating motion of a tappet connected to a hinged wastegate and/or to a variable turbine geometry device of an exhaust gas turbocharger. The tappet and/or an axle between the tappet and the threaded element is received in at least one guide comprising at least one web and allowing for at least a slight tilting or pivoting movement of the tappet in at least one direction. At least some play is present between the web and at least one broadened portion on the tappet and/or on the axle. Methods of actuating a wastegate and/or a variable turbine geometry device.